One of my close collateral Ancestors, John Crosbie, was in fact a member of the Irish House of Lords, as Earl of Glandore, but it was abolished in 1801 and he became a member of Westminster Lords. He was indeed elected - as a "representative peer" by the other Irish Lords. Says wiki:I'm against the unelected House of Lords. But you're letting your prejudice show again - it's the good ole English, Welsh, Scottish, and Northern Irish democracy that props up the good ole English, Welsh, Scottish, and Northern Irish House of Lords.
... he was elected for both Tralee and Ardfert. He chose to sit for the latter, and held the seat until 1781, when he succeeded his father in the earldom and entered the Irish House of Lords. He was sworn of the Irish Privy Council in 1785. In 1789, he was appointed Joint Master of the Rolls in Ireland alongside the Earl of Carysfort. They both held the post until 1801. In 1800, he was elected as one of the 28 original Irish Representative Peers to sit in the House of Lords.
But I really can't see how democracy in the minority countries of the UK props up English Lords nowadays, whatever may have been the arrangement in 1801.